We present direct numerical simulations of inhomogeneous reduced
magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfv\'en critical
point. These are the first such simulations that take into account the
solar-wind outflow velocity and the radial inhomogeneity of the background
solar wind without approximating the nonlinear terms in the governing
equations. RMHD turbulence is driven by outward-propagating Alfv\'en waves
($z^+$ fluctuations) launched from the Sun, which undergo partial non-WKB
reflection to produce sunward-propagating Alfv\'en waves ($z^-$ fluctuations).
We present ten simulations with different values of the correlation time
$\tau_{\rm c\,\sun}^+$ and perpendicular correlation length $L_{\perp \sun}$ of
outward-propagating Alfv\'en waves (AWs) at the coronal base. We find that
between 15% and 33% of the $z^+$ energy launched into the corona dissipates
between the coronal base and Alfv\'en critical point. Between 33% and 40% of
this input energy goes into work on the solar-wind outflow, and between 22% and
36% escapes as $z^+$ fluctuations through the simulation boundary at $r=r_{\rm
A}$. The $z^\pm$ power spectra scale like $k_\perp^{-\alpha^\pm}$, where
$k_\perp$ is the wavenumber in the plane perpendicular to $\vec{B}_0$. In our
simulation with the smallest value of $\tau_{\rm c\,\sun}^+$ ($\sim 2
\mbox{min}$) and largest value of $L_{\perp \sun}$ ($2\times 10^4 \mbox{km}$),
we find that $\alpha^+$ decreases approximately linearly with increasing
$\ln(r)$, reaching a value of 1.3 at $r=11.1 R_{\sun}$. Our simulations with
larger values of $\tau_{\rm c\,\sun}^+$ exhibit alignment between the contours
of constant $\phi^+$, $\phi^-$, $\Omega_0^+$, and $\Omega_0^-$, where
$\phi^\pm$ are the Els\"asser potentials and $\Omega_0^\pm$ are the outer-scale
parallel Els\"asser vorticities.